Solve for a
a=\frac{x}{x-1}
x\neq 1
Solve for x
x=\frac{a}{a-1}
a\neq 1
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2ax-a-a=2x
Subtract a from both sides.
2ax-2a=2x
Combine -a and -a to get -2a.
\left(2x-2\right)a=2x
Combine all terms containing a.
\frac{\left(2x-2\right)a}{2x-2}=\frac{2x}{2x-2}
Divide both sides by 2x-2.
a=\frac{2x}{2x-2}
Dividing by 2x-2 undoes the multiplication by 2x-2.
a=\frac{x}{x-1}
Divide 2x by 2x-2.
2ax-a-2x=a
Subtract 2x from both sides.
2ax-2x=a+a
Add a to both sides.
2ax-2x=2a
Combine a and a to get 2a.
\left(2a-2\right)x=2a
Combine all terms containing x.
\frac{\left(2a-2\right)x}{2a-2}=\frac{2a}{2a-2}
Divide both sides by 2a-2.
x=\frac{2a}{2a-2}
Dividing by 2a-2 undoes the multiplication by 2a-2.
x=\frac{a}{a-1}
Divide 2a by 2a-2.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}